topic badge

7.04 Range and interquartile range (IQR)

Worksheet
Range
1

Find the range of the following sets of scores:

a
6,\, 2,\, 9,\, 6,\, 1,\, 7,\, 8,\, 4
b
41, \,48, \,53, \,54, \,59, \,40, \,39, \,55, \,50
c
10, \, 7, \, 2, \, 14, \, 13, \, 15, \, 11, \, 4
d
164,\, 180,\, 127,\, 130,\, 154,\, 109
e
70,\, 68,\, 90,\, 54,\, 87,\, 66,\, 99,\, 52,\, 68
f
-8, \, -10, \, -4, \, -7, \, -2, \, -5, \, 0, \, -4, \, 2
g
6.34,\, 7.25,\, 6.90,\, 7.05,\, 4.68,\, 5.69,\, 3.25
h
1.2703, \, 1.4267, \, 1.2500, \, 1.2703, \, 0.3309, \, 1.4267, \, 0.7080
2

Consider the data provided in the table:

a

Find the range of the scores.

b

State the mode.

ScoreFrequency
6816
6941
7030
7131
7249
7329
3

Which sets of data have the same range?

  • Set A: \, 3, \, 10, \, 12, \, 20, \, 24

  • Set B: \, 8, \, 21, \, 34, \, 61

  • Set C: \, 16, \, 25, \, 33

  • Set D: \, 1, \, 11, \, 20, \, 22

4

Which set of data has the smallest range?

  • Set A: \, 13, \, 16, \, 19, \, 21, \, 24

  • Set B: \, 15, \, 24, \, 50, \, 58

  • Set C: \, 6, \, 8, \, 16, \, 35, \, 40

  • Set D: \, 8, \, 14, \, 19, \, 24, \, 28

5

Which set of data has the largest range?

  • Set A: \,101,\, 105,\, 118,\, 129,\, 136

  • Set B: \,19,\, 23,\, 25,\, 28,\, 29

  • Set C: \,22,\, 25,\, 43,\, 45,\, 57

  • Set D: \,104,\, 107,\, 113,\, 128,\, 141

6

A group of students had a range in scores of 14 and the least score was 9. Find the greatest score in the group.

7

The range of a set of scores is 8, and the greatest score is 19. Find the least score in the set.

Interquartile range
8

Here are Paul's scores from his last 13 rounds of golf played:64, \, 66, \, 68, \, 70, \, 72, \, 74, \, 78, \, 84, \, 102, \, 106, \, 112, \, 124, \, 128

a

Find his median score.

b

Find the lower quartile score.

c

Find the upper quartile score.

9

Here are Adam's scores from his last 17 exams:38, \, 44, \, 48, \, 51, \, 56, \, 58, \, 62, \, 70, \, 74, \, 78, \, 80, \, 82, \, 85, \, 88, \, 92, \, 94, \, 100

a

Find his median score.

b

Find the lower quartile score.

c

Find the upper quartile score.

10

Consider the following set of scores:

33,\, 38,\, 50,\, 12,\, 33,\, 48,\, 41

a

Sort the scores in ascending order.

b

Find the number of scores.

c

Find the median.

d

Find the first quartile.

e

Find the third quartile.

f

Find the interquartile range.

11

Consider the following set of scores:

13,\, 15,\, 5,\, 16,\, 7,\, 20,\, 12

a

Sort the scores in ascending order.

b

Find the number of scores.

c

Find the median.

d

Find the range.

e

Find the first quartile.

f

Find the third quartile.

g

Find the interquartile range.

12

Consider the given frequency table:

a

Sort the scores in ascending order.

b

Find the number of scores.

c

Find the median.

d

Find the first quartile.

e

Find the third quartile.

f

Find the interquartile range.

ScoreFrequency
53
133
162
282
313
384
482
13

In a competition, a contestant must complete 12 challenges earning as many points as possible. Her scores for the first 11 challenges are:

32,\, 38,\, 45,\, 55,\, 66,\, 86,\, 94,\, 98,\, 106,\, 108,\, 117

Find her score in the 12th round if the lower quartile of all of her 12 scores is 47.5.

Sign up to access Worksheet
Get full access to our content with a Mathspace account

Outcomes

MA.6.DP.1.2

Given a numerical data set within a real-world context, find and interpret mean, median, mode and range.

MA.6.DP.1.3

Given a box plot within a real-world context, determine the minimum, the lower quartile, the median, the upper quartile and the maximum. Use this summary of the data to describe the spread and distribution of the data.

What is Mathspace

About Mathspace